Geometric and topological approaches to significance testing in wavelet analysis
Geometric and topological methods are applied to significance testing in the wavelet domain. A geometric test was developed for assigning significance to pointwise significance patches in local wavelet spectra, i.e., contiguous regions of significant wavelet power coefficients with respect to some n...
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ftdoajarticles:oai:doaj.org/article:20ceb17eaace4c44bf4fd4ba030c7749 2023-05-15T17:34:54+02:00 Geometric and topological approaches to significance testing in wavelet analysis J. A. Schulte C. Duffy R. G. Najjar 2015-03-01T00:00:00Z https://doi.org/10.5194/npg-22-139-2015 https://doaj.org/article/20ceb17eaace4c44bf4fd4ba030c7749 EN eng Copernicus Publications http://www.nonlin-processes-geophys.net/22/139/2015/npg-22-139-2015.pdf https://doaj.org/toc/1023-5809 https://doaj.org/toc/1607-7946 1023-5809 1607-7946 doi:10.5194/npg-22-139-2015 https://doaj.org/article/20ceb17eaace4c44bf4fd4ba030c7749 Nonlinear Processes in Geophysics, Vol 22, Iss 2, Pp 139-156 (2015) Science Q Physics QC1-999 Geophysics. Cosmic physics QC801-809 article 2015 ftdoajarticles https://doi.org/10.5194/npg-22-139-2015 2022-12-31T10:13:54Z Geometric and topological methods are applied to significance testing in the wavelet domain. A geometric test was developed for assigning significance to pointwise significance patches in local wavelet spectra, i.e., contiguous regions of significant wavelet power coefficients with respect to some noise model. This geometric significance test was found to produce results similar to an existing areawise significance test while being more computationally flexible and efficient. The geometric significance test can be readily applied to pointwise significance patches at various pointwise significance levels in wavelet power and coherence spectra. The geometric test determined that features in wavelet power of the North Atlantic Oscillation (NAO) are indistinguishable from a red-noise background, suggesting that the NAO is a stochastic, unpredictable process, which could render difficult the future projections of the NAO under a changing global system. The geometric test did, however, identify features in the wavelet power spectrum of an El Niño index (Niño 3.4) as distinguishable from a red-noise background. A topological analysis of pointwise significance patches determined that holes, deficits in pointwise significance embedded in significance patches, are capable of identifying important structures, some of which are undetected by the geometric and areawise tests. The application of the topological methods to ideal time series and to the time series of the Niño 3.4 and NAO indices showed that the areawise and geometric tests perform similarly in ideal and geophysical settings, while the topological methods showed that the Niño 3.4 time series contains numerous phase-coherent oscillations that could be interacting nonlinearly. Article in Journal/Newspaper North Atlantic North Atlantic oscillation Directory of Open Access Journals: DOAJ Articles Nonlinear Processes in Geophysics 22 2 139 156 |
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Directory of Open Access Journals: DOAJ Articles |
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ftdoajarticles |
language |
English |
topic |
Science Q Physics QC1-999 Geophysics. Cosmic physics QC801-809 |
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Science Q Physics QC1-999 Geophysics. Cosmic physics QC801-809 J. A. Schulte C. Duffy R. G. Najjar Geometric and topological approaches to significance testing in wavelet analysis |
topic_facet |
Science Q Physics QC1-999 Geophysics. Cosmic physics QC801-809 |
description |
Geometric and topological methods are applied to significance testing in the wavelet domain. A geometric test was developed for assigning significance to pointwise significance patches in local wavelet spectra, i.e., contiguous regions of significant wavelet power coefficients with respect to some noise model. This geometric significance test was found to produce results similar to an existing areawise significance test while being more computationally flexible and efficient. The geometric significance test can be readily applied to pointwise significance patches at various pointwise significance levels in wavelet power and coherence spectra. The geometric test determined that features in wavelet power of the North Atlantic Oscillation (NAO) are indistinguishable from a red-noise background, suggesting that the NAO is a stochastic, unpredictable process, which could render difficult the future projections of the NAO under a changing global system. The geometric test did, however, identify features in the wavelet power spectrum of an El Niño index (Niño 3.4) as distinguishable from a red-noise background. A topological analysis of pointwise significance patches determined that holes, deficits in pointwise significance embedded in significance patches, are capable of identifying important structures, some of which are undetected by the geometric and areawise tests. The application of the topological methods to ideal time series and to the time series of the Niño 3.4 and NAO indices showed that the areawise and geometric tests perform similarly in ideal and geophysical settings, while the topological methods showed that the Niño 3.4 time series contains numerous phase-coherent oscillations that could be interacting nonlinearly. |
format |
Article in Journal/Newspaper |
author |
J. A. Schulte C. Duffy R. G. Najjar |
author_facet |
J. A. Schulte C. Duffy R. G. Najjar |
author_sort |
J. A. Schulte |
title |
Geometric and topological approaches to significance testing in wavelet analysis |
title_short |
Geometric and topological approaches to significance testing in wavelet analysis |
title_full |
Geometric and topological approaches to significance testing in wavelet analysis |
title_fullStr |
Geometric and topological approaches to significance testing in wavelet analysis |
title_full_unstemmed |
Geometric and topological approaches to significance testing in wavelet analysis |
title_sort |
geometric and topological approaches to significance testing in wavelet analysis |
publisher |
Copernicus Publications |
publishDate |
2015 |
url |
https://doi.org/10.5194/npg-22-139-2015 https://doaj.org/article/20ceb17eaace4c44bf4fd4ba030c7749 |
genre |
North Atlantic North Atlantic oscillation |
genre_facet |
North Atlantic North Atlantic oscillation |
op_source |
Nonlinear Processes in Geophysics, Vol 22, Iss 2, Pp 139-156 (2015) |
op_relation |
http://www.nonlin-processes-geophys.net/22/139/2015/npg-22-139-2015.pdf https://doaj.org/toc/1023-5809 https://doaj.org/toc/1607-7946 1023-5809 1607-7946 doi:10.5194/npg-22-139-2015 https://doaj.org/article/20ceb17eaace4c44bf4fd4ba030c7749 |
op_doi |
https://doi.org/10.5194/npg-22-139-2015 |
container_title |
Nonlinear Processes in Geophysics |
container_volume |
22 |
container_issue |
2 |
container_start_page |
139 |
op_container_end_page |
156 |
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1766133872632791040 |